Question

You have won a contest and will receive $2,500 a year in real terms for the next 3 years. Each payment will be received at the end of the period with the first payment occurring one year from today. The relevant nominal discount rate is 6.3 percent and the inflation rate is 4.5 percent. What are your winnings worth today?

Answer 1

To find the present value of an annuity of $2,500 received over 3 years with given nominal and inflation rates, calculate the real rate, discount each payment back to present value, and sum these values.

Step-by-step explanation:

The student has asked to calculate the present value of $2,500 received annually for 3 years given a nominal discount rate of 6.3 percent and an inflation rate of 4.5 percent. To calculate the present value of the winnings, we must first determine the real discount rate using the Fisher Equation, which gives us the formula (1 + nominal rate) = (1 + real rate) * (1 + inflation rate). Therefore, the real discount rate is approximately 1.73%. Using this rate, we can discount each of the $2,500 payments back to present value using the formula PV = C/(1+r)^t where PV is the present value, C is the cash flow (payment), r is the discount rate, and t is the time period.

For the first year's payment, t=1, for the second year's payment, t=2, and for the third year's payment, t=3. Performing these calculations gives us the present values for these payments, which we then sum to find the total present value of the winnings available today.